"There are some small local Taliban groups who have agreed not to create any problem on election day. The elders have convinced them that this is against the interests of the people and of Pashtuns," he said.
The Taliban leadership has called the election, due next Thursday, an American invention, and has threatened to disrupt voting across the country.
Qari Yusuf, a Taliban spokesman in the south, denied that agreements about a truce on the day of the vote had been made.
"If we accept the election, then we give legitimacy to the government and allow the invaders to invade our country," he told Al Jazeera.
"I am 100 per cent sure even low-level commanders won't be traitors. Whatever Ahmed Wali said is propaganda."
According to the United Nations, violence and intimidation have already disrupted planning and campaigning in the south of the country, and could prevent many Afghans from casting their ballots.
Election officials have said fears of violence could prevent hundreds of polling stations from opening and that voting was unlikely in nine of 365 districts.
Violence has surged in the weeks before the vote, with fighters staging a number of attacks on provincial government buildings in the south, and also launching raids in the north and west.
Taliban fighters clashed with police in the northern province of Baghlan late on Friday, killing five people, including two children, police said.
Opinion polls have indicated that Hamid Karzai leads the presidential race, but without enough support to win an outright majority.
The US-funded International Republican Institute released poll results on Friday, suggesting Karzai would win 44 per cent of the vote while his main challenger Abdullah Abdullah, a former foreign minister, would win 26 per cent.
If no candidate wins more than 50 per cent in the first round, a runoff will be held between the top two.
In parallel with the presidential poll, Afghans will also vote for provincial councils.